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Analysis of local discontinuous Galerkin method for time–space fractional convection–diffusion equations

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Abstract

This paper focuses on the time–space fractional convection–diffusion equations with time fractional derivative (of order \(\alpha \), \(0< \alpha <1\)) and space fractional derivative (of order \(\beta \), \(1<\beta <2\)). An approach based on a combination of local discontinuous Galerkin (in space) and finite difference methods (in time) is presented to solve the fractional convection–diffusion equations. The stability and convergence analysis of the method are given. Numerical results confirm the theory of the method for fractional convection–diffusion equations.

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Acknowledgements

We would like to thank anonymous referees for carefully reading the manuscript and for their valuable comments and suggestions, which helped us to considerably improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Qom, Isfahan Old Road, Qom, Iran

    M. Ahmadinia & Z. Safari

  2. Department of Mathematics, University of Shahrekord, Shahrekord, Iran

    S. Fouladi

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  1. M. Ahmadinia
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  2. Z. Safari
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  3. S. Fouladi
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Correspondence to M. Ahmadinia.

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Communicated by Jan Hesthaven.

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Ahmadinia, M., Safari, Z. & Fouladi, S. Analysis of local discontinuous Galerkin method for time–space fractional convection–diffusion equations. Bit Numer Math 58, 533–554 (2018). https://doi.org/10.1007/s10543-018-0697-x

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  • DOI: https://doi.org/10.1007/s10543-018-0697-x

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